{"id":"https://openalex.org/W620457302","doi":null,"title":"Low Rank States with Bound Entanglement in a System of three qubits","display_name":"Low Rank States with Bound Entanglement in a System of three qubits","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W620457302","mag":"620457302"},"language":"en","primary_location":{"id":"pmh:oai:brage.bibsys.no:11250/247195","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/247195","pdf_url":"http://hdl.handle.net/11250/247195","source":{"id":"https://openalex.org/S4306400255","display_name":"BIBSYS Brage (BIBSYS (Norway))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I173212132","host_organization_name":"Vilnius University","host_organization_lineage":["https://openalex.org/I173212132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"81","raw_type":"Master thesis"},"volume":null,"type":"dissertation","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11250/247195","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052772651","display_name":"B\u00f8rge Irgens","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"B\u00f8rge Irgens","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5052772651"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9746000170707703,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.01549999974668026,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.0027000000700354576,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bound-entanglement","display_name":"bound entanglement","score":0.902999997138977},{"id":"https://openalex.org/keywords/three-qubit-systems","display_name":"three-qubit systems","score":0.8059999942779541},{"id":"https://openalex.org/keywords/partial-transpose","display_name":"partial transposition","score":0.8299999833106995},{"id":"https://openalex.org/keywords/lorentz-invariants","display_name":"Lorentz invariants","score":0.8289999961853027},{"id":"https://openalex.org/keywords/separable-states","display_name":"separable states","score":0.8500000238418579},{"id":"https://openalex.org/keywords/extremal-states","display_name":"extremal states","score":0.6480000019073486},{"id":"https://openalex.org/keywords/symmetric-states","display_name":"symmetric states","score":0.4129999876022339}],"concepts":[{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.6656648516654968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.579988956451416},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5798068046569824},{"id":"https://openalex.org/C5667645","wikidata":"https://www.wikidata.org/wiki/Q217255","display_name":"Lorentz transformation","level":2,"score":0.5495242476463318},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.5236817598342896},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.500758171081543},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.46909913420677185},{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.4396573603153229},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41959893703460693},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33679211139678955},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2665908932685852},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19375404715538025},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1856744885444641},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1513272523880005},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:brage.bibsys.no:11250/247195","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/247195","pdf_url":"http://hdl.handle.net/11250/247195","source":{"id":"https://openalex.org/S4306400255","display_name":"BIBSYS Brage (BIBSYS (Norway))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I173212132","host_organization_name":"Vilnius University","host_organization_lineage":["https://openalex.org/I173212132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"81","raw_type":"Master thesis"},{"id":"pmh:oai:ntnuopen.ntnu.no:11250/247195","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/247195","pdf_url":null,"source":{"id":"https://openalex.org/S7407064446","display_name":"NORA - Norwegian Open Research Archives","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"81","raw_type":"info:eu-repo/semantics/masterThesis"},{"id":"mag:620457302","doi":null,"is_oa":false,"landing_page_url":"https://brage.bibsys.no/xmlui/handle/11250/247195","pdf_url":null,"source":{"id":"https://openalex.org/S4363604979","display_name":"81","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"other"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"81","raw_type":null}],"best_oa_location":{"id":"pmh:oai:brage.bibsys.no:11250/247195","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11250/247195","pdf_url":"http://hdl.handle.net/11250/247195","source":{"id":"https://openalex.org/S4306400255","display_name":"BIBSYS Brage (BIBSYS (Norway))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I173212132","host_organization_name":"Vilnius University","host_organization_lineage":["https://openalex.org/I173212132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"81","raw_type":"Master thesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W620457302.pdf","grobid_xml":"https://content.openalex.org/works/W620457302.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W382604833","https://openalex.org/W1586863949","https://openalex.org/W1738124305","https://openalex.org/W1968144792","https://openalex.org/W1983951216","https://openalex.org/W1986407511","https://openalex.org/W2026792714","https://openalex.org/W2032622350","https://openalex.org/W2034920898","https://openalex.org/W2037757747","https://openalex.org/W2049681112","https://openalex.org/W2051786477","https://openalex.org/W2064377015","https://openalex.org/W2073384645","https://openalex.org/W2082377311","https://openalex.org/W2135830616","https://openalex.org/W2148576428","https://openalex.org/W2154434103","https://openalex.org/W2481251364","https://openalex.org/W2593968316"],"related_works":["https://openalex.org/W1983951216","https://openalex.org/W2698843518","https://openalex.org/W2964326670","https://openalex.org/W2049681112","https://openalex.org/W7161828742","https://openalex.org/W382604833","https://openalex.org/W2007048219","https://openalex.org/W2026792714","https://openalex.org/W1586863949","https://openalex.org/W2802494937"],"abstract_inverted_index":{"We":[0,27,45,105,154,222],"have":[1,46,125,195],"studied":[2,47],"mixed":[3],"quantum":[4],"states":[5,94,110,123,160,217,225,245],"in":[6,132,176,246],"the":[7,13,33,36,49,100,119,148,177,200,238,241],"system":[8],"of":[9,35,62,93,109,111,147,159,180,212,226,232,243],"three":[10,41],"qubits":[11],"with":[12],"property":[14],"that":[15,172,224],"all":[16,118],"their":[17],"partial":[18,43,152,169,191],"transposes":[19],"are":[20,23,128,141,164,187],"positive;":[21],"these":[22],"called":[24],"PPT":[25,30,56,122,216],"states.":[26],"classify":[28],"a":[29,68,133,173,181,190],"state":[31,37,149,174,183,201],"by":[32,67],"ranks":[34],"itself":[38],"and":[39,52,97,150,193,210],"its":[40,151,185,203],"single":[42],"transposes.":[44,153],"especially":[48],"rank":[50,53,63,120,214,233],"4444":[51],"5555":[54,215,234],"entangled":[55],"states.We":[57],"find":[58,155,171,223],"two":[59],"distinct":[60,157],"classes":[61,158],"four":[64,121,156],"states,":[65],"identified":[66],"real":[69],"valued":[70],"quadratic":[71,85],"expression":[72],"invariant":[73,87],"under":[74,168,189],"local":[75],"$\\\\sln$":[76],"transformations,":[77],"mathematically":[78],"equivalent":[79],"to":[80,116,143,198],"continuous":[81],"Lorentz":[82,86,207],"transformations.":[83],"This":[84],"is":[88,175],"non-zero":[89],"for":[90,99],"one":[91],"class":[92,102,179],"(type":[95,103],"1)":[96],"zero":[98],"other":[101],"2).":[104],"present":[106],"analytical":[107],"constructions":[108],"both":[112],"types,":[113],"general":[114],"enough":[115],"reproduce":[117],"we":[124,194],"found":[126],"numerically.There":[127],"six":[129],"product":[130,139],"vectors":[131,140],"generic":[134],"five":[135],"dimensional":[136],"subspace.":[137],"The":[138],"used":[142],"define":[144],"SL":[145],"invariants":[146,163,186],"based":[161],"which":[162],"conserved":[165,188],"or":[166],"not":[167],"transposition.We":[170],"equivalence":[178],"symmetric":[182,204],"when":[184],"transposition,":[192],"shown":[196],"how":[197],"transform":[199],"into":[202],"form":[205],"through":[206],"transformations.The":[208],"dimensions":[209],"geometry":[211],"extremal":[213],"has":[218],"also":[219],"been":[220],"examined.":[221],"different":[227,235,247],"types":[228],"lie":[229],"on":[230],"surfaces":[231,239],"dimensions.":[236],"And":[237],"touch":[240],"simplex":[242],"separable":[244],"ways":[248]},"counts_by_year":[],"updated_date":"2026-09-09T07:26:56.047234","created_date":"2016-06-24T00:00:00"}